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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 213 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 136 (b) 124 (c) 248 (d) 26
  2. 2.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 15 (b) 92 (c) 96 (d) 184
  3. 3.What is the 21st term of the AP 14, 16, 18, 20, …? (a) 42 (b) 40 (c) 54 (d) 56
  4. 4.What is the 39th term of the AP 17, 25, 33, 41, …? (a) 304 (b) 321 (c) 312 (d) 329
  5. 5.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 625 (d) 49
  6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 136 (d) 272
  7. 7.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 572 (b) 291 (c) 286 (d) 51
  8. 8.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 504 (b) 252 (c) 257 (d) 48
  9. 9.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 21 (b) 22 (c) 19 (d) 20
  10. 10.Which term of the AP 14, 18, 22, 26, … is 54? (a) 13th (b) 10th (c) 12th (d) 11th
  11. 11.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 992 (c) 496 (d) 465
  12. 12.Which term of the AP 15, 20, 25, 30, … is 95? (a) 16th (b) 19th (c) 17th (d) 18th
  13. 13.Which term of the AP 1, 8, 15, 22, … is 267? (a) 41st (b) 38th (c) 39th (d) 40th
  14. 14.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 169 (d) 91
  15. 15.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2048 (c) 2080 (d) 4160
  16. 16.Which term of the AP 15, 18, 21, 24, … is 51? (a) 17th (b) 13th (c) 12th (d) 14th
  17. 17.Which term of the AP 5, 7, 9, 11, … is 65? (a) 32nd (b) 31st (c) 30th (d) 33rd
  18. 18.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 903 (c) 947 (d) 946
  19. 19.What is the sum of all the whole numbers from 1 to 15? (a) 120 (b) 240 (c) 121 (d) 105
  20. 20.Which term of the AP 13, 18, 23, 28, … is 183? (a) 37th (b) 35th (c) 34th (d) 36th
  21. 21.What is the 19th term of the AP 6, 15, 24, 33, …? (a) 168 (b) 171 (c) 162 (d) 177
  22. 22.What is the 21st term of the AP 6, 10, 14, 18, …? (a) 86 (b) 90 (c) 80 (d) 84
  23. 23.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 277 (c) 276 (d) 552
  24. 24.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 144 (b) 138 (c) 276 (d) 17
  25. 25.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 54 (b) 638 (c) 324 (d) 319
  26. 26.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 112 (b) 56 (c) 57 (d) 11
  27. 27.Which term of the AP 11, 17, 23, 29, … is 95? (a) 17th (b) 16th (c) 15th (d) 14th
  28. 28.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 528 (c) 1056 (d) 512
  29. 29.What is the 39th term of the AP 16, 23, 30, 37, …? (a) 273 (b) 289 (c) 282 (d) 266
  30. 30.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 60 (b) 64 (c) 120 (d) 11
  31. 31.Which term of the AP 10, 18, 26, 34, … is 90? (a) 13th (b) 12th (c) 10th (d) 11th
  32. 32.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
  33. 33.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 3741 (c) 7482 (d) 3698
  34. 34.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 288 (b) 144 (c) 162 (d) 39
  35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 120 (d) 225
  36. 36.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 12 (c) 114 (d) 57
  37. 37.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 15 (b) 13 (c) 14 (d) 12
  38. 38.What is the 32nd term of the AP 13, 17, 21, 25, …? (a) 128 (b) 124 (c) 137 (d) 141
  39. 39.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 20 (b) 348 (c) 180 (d) 174
  40. 40.What is the missing term in the AP 11, 17, ?, 29, 35? (a) 23 (b) 29 (c) 24 (d) 22

Answer key

  1. 124
  2. 92
  3. 54
  4. 321
  5. 625
  6. 256
  7. 286
  8. 252
  9. 20
  10. 11th
  11. 496
  12. 17th
  13. 39th
  14. 169
  15. 2080
  16. 13th
  17. 31st
  18. 946
  19. 120
  20. 35th
  21. 168
  22. 86
  23. 276
  24. 138
  25. 319
  26. 56
  27. 15th
  28. 528
  29. 282
  30. 60
  31. 11th
  32. 784
  33. 3741
  34. 144
  35. 225
  36. 57
  37. 13
  38. 137
  39. 174
  40. 23

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